Last time I have seems HP 4L printer was 5 years ago.
The printer is work hose, if your maintenance is up to part.
the plastic wheel is the inner cord of a paper roller.
you can order the part from:http://www.feedroller.com/Store/index.php?cPath=1_17_86_25
the roller is about $8. each
I suggest that you get a maintenance kit. One of the roller is gone, other parts will follow, and since you will have th printer apart, you can change the other parts that also need to be changed.

Yes. It should be cheap. Check to see if it has any gears that a piece may have been broken off of. That could be the reason why it will not spin to pull the paper in, or a cord may be broken that gives power to the wheel. Check to see if you see any dangling wires that are near the wheel. You will most likely need to get this professionally done to ensure that no other problems occur if you try to do it yourself that will cause the printer to mess up even worse.

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Clean The Paper Feed Rollers (Windows)
Instructions how to clean the paper feed rollers. If the paper feed rollers become dirty, they may not be able to properly feed paper due to the feed roller's slippage. If paper does not feed correctly, perform the following to clean the paper feed rollers:

Open the printer properties.

Click the 'Maintenance' tab and click 'Roller Cleaning'.

Remove all sheets of paper from the auto sheet feeder.

Confirm the following message, and click 'OK'.

Note: Clicking 'OK' will activate the paper feed rollers 30 times. Thisactivation will take about 90 seconds. Do not perform other operationsuntil this operation has finished.

Confirm the following message, and click 'OK'.

After the continuous paper feeding operations in step 5 have finished, load three sheets of plain paper and click 'OK'.

Confirm the following message, and click 'OK'.

Note: The following message is displayed when the paper is fed and ejected.

You say the paper is scewed to the right which means absolutely nothing if you think about it, isn't the left hand side also scewed? Usually one side of the paper is pulled down leaving the other side up thus scewing it. Firstly make sure nothing has fallen down the paper slot, secondly make sure the sliding paper adjuster to the left of the paper is up tight against the paper, even a 1 millimetre gap can cause this problem, thirdly look down the paper slot with the paper in and make sure there is no gap between the bottom edge of paper and plastic shute or case, you really shouldn't be able to see much of the two pieces of white plastic, now press the green start button.

take a look inside the printer there are a few small rubber wheels (where paper comes out)
most likely you have a small piece of paper jammed and blocking the left wheel from pulling the paper. they are very delicate so be gentle with them. the issue may also be caused from the back set of wheels where the paper feeds into the printer.
I have a straight piece if clear plastic thet is approx same size as sheet of paper and this is what I use to clear paper jams. The best way to prevent this from happening again is to remove paper when not using and cover printer with a small towel. I have found p-clips and all sorts of junk in clinets printers.

I kept running the maintenance roller cleaning with paper in the feed and eventually I was able to see the tip of the plastic piece that had fallen in as I pulled the paper through with my fingers, I was able to get the whole piece and now the printer is golden.

Cut the paper off clean.
Slid it through the slot on the back.
The place the paper between the black plastic rail,
and the bottom of the calculator.
Keep feeding it in the slot untill you can see it under the
foam wheel.
The repedably hit the feed button until the paper comes
out the other side.
If it does not feed, the paper is not under the wheel far enough.
This should work on other similar models as well.

Check encoder disc if it is stained with ink or broken (its the round foil disc which is fixed on one of the three white big gear wheels on the left hand side). It should turn around without any scratching sound!

Check if another gear wheel is broken (right hand side behind the purge /parking station). Here you will find the gear box which is shifted by print head (little white plastic coming out of the metal plate between purge station and absorber box)

Pull out the paper tray and try to turn the paper feed roller by hand. You can reach it when seeing from bottom without the tray.

Feed the paper manually into the printer:Place a sheet of plain A4 paper in the paper feed tray. Move the paper support on the left-hand side to the left end of the paper.Press the paper feed button.If the paper does not feed, continue with step 2.

Check for any obstructions in the paper feed path:Disconnect the cables from the back of the printer.Open the front of the printer and check for anything that may be blocking the paper path.Close the front lid and remove any paper from the paper feed tray.Holding the printer in both hands, turn it upside down to see if anything falls out of the paper feed area. (Sometimes objects such as pens, paper clips and so on can fall into the paper feed area and cause blockages.)

Check for any pieces of torn paper in the path, especially on the left side. You can also reach into the slot that the paper feeds into and feel each of the rollers behind the plastic cover; they all should turn freely, pay special attention to the wheel to the left.